Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens. Part II: 3-D effects on constraint

This study describes an extensive set of 3-D analyses conducted on conventional fracture specimens, including pin-loaded and clamped SE(T) specimens, and axially cracked pipes with varying crack configurations. The primary objective is to examine 3-D effects on the correlation of fracture behavior for the analyzed crack configurations using the J-Q methodology. An average measure of constraint over the crack front, as given by an average hydrostatic parameter, denoted Q_avg, is employed to replace the plane-strain measure of constraint, Q. Alternatively, a local measure of constraint evaluated at the mid-thickness region of the specimen, denoted Q_Z0, is also utilized. The analysis matrix considers 3-D numerical solutions for models of SE(T) fracture specimens with varying geometries (i.e., different crack depth to specimen width ratio, a/W, as well as different loading point distance, H) and test conditions (pin-loaded ends vs. clamped ends). The 3-D numerical models for the cracked pipes cover different crack depth to pipe wall thickness ratio, a/t, and a fixed crack depth to crack length ratio, a/c. The extensive 3-D numerical analyses presented here provide a representative set of solutions which provide further support for using constraint-designed SE(T) specimens in fracture assessments of pressurized pipes and cylindrical vessels.     

Fracture toughness of high strength seamless pipe steel from SE(T) and SE(B) specimens evaluated by different standards

Recently released, BS 8571:2014 standard offers an alternative for the experimental determination of fracture toughness and resistance curves of metallic materials from SE(T) specimens. Similar in stress conditions and constraint to cracked tubes, specimens in SE(T) geometry should yield less conservative toughness values than conventional high‐constraint specimens, such as SE(B) geometry. However, the convention to determine the J‐integral fracture toughness proposed in the new BS standard is different from ASTM standards. In this work, SE(T) and SE(B) specimens of similar dimensions of a tough high‐strength seamless pipe steel were tested following the BS 8571:2014 and ASTM E1820‐16 standards, respectively. Because of the different standardized definitions, SE(T) specimens yield lower fracture toughness than SE(B) specimens, which could lead to more conservative results in structural integrity analysis. This investigation also suggests the introduction of the blunting line concept in the BS 8571:2014 standard in order to minimize this problem.     

Numerical investigation of 3-D constraint effects on brittle fracture in SE(B) and C(T) specimens

Specimen size and geometry effects on cleavage fracture of ferritic steels tested in the ductile-to-brittle transition region remain an important technological impediment in industrial applications of fracture mechanics and in the on-going development of consensus fracture testing standards. This investigation employs 3-D nonllinear finite element analyses to conduct an extensive parametric evaluation of crack front stress triaxiality for deep notch SE(B) and C(T) specimens and shallow notch SE(B) specimens, with and without side grooves. Crack front conditions are characterized in terms of J-Q trajectories and the constraint model for cleavage fracture toughness proposed previously by Dodds and Anderson. An extension of the toughness scaling model suggested here combines a revised in-plane constraint correction with an explicit thickness correction derived from extreme value statistics. The 3-D analyses provide effective thicknesses for use in the statistical correction which reflect the interaction of material flow properties and specimen aspect ratios, a/W and W/B, on the varying levels of stress triaxiality over the crack front. The 3-D computational results imply that a significantly less strict size/deformation limit, relative to the limit indicated by previous plane-strain computations, is needed to maintain small-scale yielding conditions at fracture by a stress-controlled, cleavage mechanism in deep notch SE(B) and C(T) speciments. Moreover, the analyses indicate that side grooves (20 percent) should have essentially no net effect on measured toughness values of such specimens. Additional new results made available from the 3-D analyses also include revised -plastic factors for use in experimental studies to convert measured work quantities to thickness average and maximum (local) J-values over the crack front. To estimate CTOD values, new m-factors are included for use in the expression 131-1.     

Estimation procedure of J-resistance curves for SE(T) fracture specimens using unloading compliance

This work provides an estimation procedure to determine J-resistance curves for pin-loaded and clamped SE(T) fracture specimens using the unloading compliance technique and the η-method. A summary of the methodology upon which J and crack extension are derived sets the necessary framework to determine crack resistance data from the measured load vs. displacement curves. The extensive plane-strain analyses enable numerical estimates of the nondimensional compliance, μ, and parameters η and γ for a wide range of specimen geometries and material properties characteristic of structural and pipeline steels. Laboratory testing of an API 5L X60 steel at room temperature using pin-loaded SE(T) specimens with side-grooves provide the load-displacement data needed to validate the estimation procedure for measuring the crack growth resistance curve for the material. The results presented here produce a representative set of solutions which lend further support to develop standard test procedures for constraint-designed SE(T) specimens applicable in measurements of crack growth resistance for pipelines.     

Two-parameter characterization of elastic-plastic crack front fields: Surface cracked plates under tensile loading

In this paper the J-Q two-parameter characterization of elastic-plastic crack front fields is examined for surface cracked plates under uniaxial and biaxial tensile loadings. Extensive three-dimensional elastic-plastic finite element analyses were performed for semi-elliptical surface cracks in a finite thickness plate, under remote uniaxial and biaxial tension loading conditions. Surface cracks with aspect ratios a/c = 0.2, 1.0 and relative depths a/t = 0.2, 0.6 were investigated. The loading levels cover from small-scale to large-scale yielding. In topological planes perpendicular to the crack fronts, the crack stress fields were obtained. In order to facilitate the determination of Q-factors, modified boundary layer analyses were also conducted. The J-Q two-parameter approach was then used in characterizing the elastic-plastic crack front stress fields along these 3D crack fronts. Complete distributions of the J-integral and Q-factors for a wide range of loading conditions were obtained. It is found that the J-Q characterization provides good estimate for the constraint loss for crack front stress fields. It is also shown that for medium load levels, reasonable agreements are achieved between the T-stress based Q-factors and the Q-factors obtained from finite element analysis. These results are suitable for elastic-plastic fracture mechanics analysis of surface cracked plates.     

Enhanced fracture assessment under biaxial external loads using small scale cruciform bending specimens

The present study is concerned with an enhanced fracture mechanics characterization of engineering materials using small scale cruciform bending specimens. Based on the regular SE(B) specimen geometry with a shallow crack, two additional loading legs allow the application of an additional stress component acting longitudinally to the crack front. Compared to standard specimen types, the biaxial loading conditions for the cruciform specimens are in general closer to the situation in pressurized vessels and pipes, especially under thermal shock loading conditions. In a combined experimental and numerical approach, detailed assessments of the local stress and strain fields in comparison to the crack front stress and strain states of standard specimens with deep and shallow cracks are provided. The cruciform bending specimen geometry is demonstrated to be suitable even in small scale dimensions. It permits the application of different combined external loading situations and thus a fracture assessment under conditions close to various situations in engineering application. Due to its small size, the specimen geometry can be employed even if only a limited amount of material is available.     

Ductile crack growth and constraint in pipelines subject to combined loadings

An important failure mode of offshore pipelines is ductile fracture of the pipe wall triggered by a hypothetical welding defect. In this study, pipelines having an external part-through semi-circumferential crack of various sizes, subject to combined internal pressure and inelastic bending are considered. This is done to assess the response of pipelines during both their installation and operational conditions. Detailed 3D nonlinear finite element (FE) models of pipelines are developed. A row of elements ahead of the initial crack front are modeled using a voided plasticity material model, which enables simulation of crack growth and the subsequent fracture failure mode (denoted by the critical curvature, κ_crit). After discussing the typical response characteristics of such pipelines, the FE model is used to parametrically investigate the influence of varying pipe and crack dimensions, and also the internal pressure levels, on κ_crit. In the second part of this paper, the crack tip constraint ahead of a growing crack in such pipes is evaluated and systematically compared to the crack tip constraint of both the traditionally used deeply cracked Single Edge Notch Bend (SENB) specimens and the constraint-matched Single Edge Notch Tensile (SENT) specimens. This is achieved by comparing the crack resistance curves (R-curves) along with stress triaxiality and equivalent plastic strain fields evaluated ahead of a growing crack of the three systems. The results present grounds for justification of usage of SENT specimens in fracture assessment of such pipes as an alternative to the traditional overly conservative SENB specimens.     

Plastic limit load and its application to the fracture toughness testing for heterogeneous single edge notch tension specimens

The current investigation pursues the confirmation of the applicability of the limit load solutions in determination of the η factors necessary for fracture toughness testing protocols. The procedure begins with the correct calculation of limit load values in welded single edge notch tension (SE(T)) fracture specimens containing centreline cracks. Hence, the η factor is inferred through the principle of potential energy. Additionally, such results are compared with those obtained from finite element analyses, including strain hardening effects available in the literature. SE(T) specimens subject to pin‐loading display that the η factors are insensitive to the configurational effects and hardening properties. On the other hand, in clamped SE(T) specimens, such effects become meaningful, making its usage in fracture toughness experiments questionable. This work provides an alternative methodology to compute fully plastic proportionality coefficients (η) based on limit load solutions for heterogeneous cracked SE(T) specimens. These analyses also consider the limitations and potentialities of such an approach in experimental measurements of ductile crack growth.     

Constraint comparisons for common fracture specimens: C(T)s and SE(B)s

New testing standards (e.g., ASTM E1921) remain under continuing development to measure the fracture toughness of ferritic steels over the ductile-to-brittle transition. The procedures assume that relatively small, deep-notch test specimens maintain near small-scale yielding conditions at fracture, which simplifies greatly the interpretation of measured values. However, 3-D finite element analyses suggest that the geometry and small size of common fracture specimens leads frequently to constraint loss, e.g., the decay of small-scale yielding conditions, at only moderate levels of deformation. The Weibull stress micromechanical model, or “local approach,” is employed here to quantify these constraint effects. Previous research along these same lines quantifies constraint loss in common fracture specimens relative to strict plane-strain, small-scale yielding conditions with a zero T-stress. Here we present a more practical approach for application within experimental testing programs by comparing directly the two most commonly tested fracture specimens, the single-edge notched bend, SE(B), and the compact tension, C(T), specimens. Developers of testing standards may thus choose a “reference” specimen then correct values measured with other specimens to the adopted reference configuration.     

The effect of residual stresses on brittle and ductile fracture initiation predicted by micromechanical models

The effect of a realistic residual stress field on the predicted initiation of brittle and ductile fracture in a pressure and axially loaded circumferentially cracked pipe is examined using finite element analysis, micromechanical models of fracture initiation, andJ-Q theory. The study confirms that residual stresses contribute to the driving force and reduce fracture loads early in the loading history. In addition, results show that the residual stresses severely alter theJ-value (i.e., fracture toughness) predicted for the onset of brittle fracture. The reason for this decrease is found to be the increase in constraint generated by the residual stress field. In contrast, the effect of residual stresses on the ductile fracture initiation toughness is shown to be negligible. kw]Key words kw]residual stress kw]fracture initiation kw]micromechanics     

On the transfer of specimen J–R curve to piping components with throughwall circumferential flaw

Transferability of the specimen J–R/J–T curve to the component level is an important issue in the field of fracture mechanics. Towards this goal, fracture experiments have been carried out on single‐edge bend (SE(B)) and compact tension (CT) specimens and throughwall circumferentially cracked straight pipes/elbows of 200 mm nominal bore (NB) diameter. The pipe material is SA 333 Gr 6 steel (low strength and high toughness material) and specimens are machined from the pipes. Subsequently, elastic–plastic finite‐element analyses have been carried out on these cracked components/specimens in order to evaluate the stress triaxiality levels. It is found that the triaxial levels for these cracked components are similar. Hence, similar fracture behaviour is expected for these components. Consequently, one of the pipe J–R curves is used as a reference J–R curve to consider the crack growth in the analysis and the load deformation behaviour of other pipes/elbows is predicted. The load deformation behaviour of the piping components is also predicted using an extrapolated J–R curve from a specimen that exhibits the similar triaxiality level to that of the cracked components. The predicted results are in good agreement with the experiments.     

Solutions of the second elastic-plastic fracture mechanics parameter in test specimens

Extensive finite element analyses have been conducted to obtain solutions of the A-term, which is the second parameter in three-term elastic-plastic asymptotic expansion, for test specimens. Three mode I crack plane-strain test specimens, i.e. single edge cracked plate (SECP), center cracked plate (CCP) and double edge cracked plate (DECP) were studied. The crack geometries analyzed included shallow to deep cracks. Solutions of A-term were obtained for material following the Ramberg-Osgood power law with hardening exponent of n = 3, 4, 5, 7 and 10. Remote tension loading was applied which covers from small-scale to large-scale yielding. Based on the finite element results, empirical equations to predict the A-terms under small-scale yielding (SSY) to large-scale yielding conditions were developed. In addition, by using the relationships between A and other commonly used second fracture parameters such as Q factor and A₂-term, the present solutions can be used to calculate parameters A₂ and Q as well. The results presented in the paper are suitable to calculate the second elastic-plastic fracture parameters for test specimens for a wide range of crack geometries, material strain hardening behaviors and loading conditions.     

Relationship between KIc and plane-strain tensile ductility and microscopic mode of fracture

In most structural steels, the critical plane-strain stress-intensity factor, K_Ic, increases markedly with increasing test temperature. Because of this transition behavior with temperature and the inherently high fracture toughness of many steels, very thick specimens must be tested to determine valid K_Ic values. The large size of these specimens and the cost of conducting the tests minimize the usefulness of this procedure as a research tool for analyzing the fracture behavior of steels under plane-strain conditions. Therefore, as part of a long-range program to obtain K_Ic values from small specimens and to extend linear-elastic fracture mechanics to the region of elastic-plastic fracture mechanics, the Research Laboratory investigated the relationship between K_Ic and ordinary tensile material properties for four steels ranging in yield strength from 80 to 250 ksi (552–1720 MN/m²).The results showed that, for these steels, the variation of K_Ic with temperature was similar to the variation of the plane-strain tensile ductility with temperature. Scanning electron micrographs showed that the increase in the plane-strain stress-intensity factor for unstable crack extension, K_Ic, with increasing temperature could be related to changes in the microscopic mode of fracture at the crack tip. That is, at temperatures below the fracture-toughness transition temperature, the mode of fracture was cleavage, whereas at temperatures well above the transition-temperature region, the fracture mode was ductile tear. In the transition-temperature region, a gradual change in fracture mode from cleavage to ductile tear occurred at the tip of the fatigue crack in the K_Ic specimens.Scanning electron micrographs of the fracture-initiation region in the plane-strain tensile-ductility specimens showed that the increase in plane-strain tensile ductility with increasing temperature for steels ranging in yield strength from 80 to 250 ksi was accompanied by a change in the microscopic mode of fracture. The change in the microscopic mode of fracture in the plane-strain tensile-ductility specimens was similar to the change observed in the crack-initiation region in the K_Ic specimens. That is, the microscopic mode of fracture in the plane-strain tensile-ductility specimens gradually changed from cleavage at cryogenic temperatures to ductile tear at room temperature. Thus, it is suggested that the increase in K_Ic with increasing temperature is caused by an increase in the plane-strain tensile ductility with increasing temperature and that this increase in ductility is related to a change in the microscopic mode of fracture from cleavage to ductile tear.     

Effects of weld strength mismatch on <Emphasis Type="Italic">J</Emphasis> and CTOD estimation procedure for SE(B) specimens

This work examines the effect of weld strength mismatch on fracture toughness measurements defined by J and CTOD fracture parameters using single edge notch bend (SE(B)) specimens. A central objective of the present study is to enlarge on previous developments of J and CTOD estimation procedures for welded bend specimens based upon plastic eta factors (η) and plastic rotational factors (r _p ). Very detailed non-linear finite element analyses for plane-strain models of standard SE(B) fracture specimens with a notch located at the center of square groove welds and in the heat affected zone provide the evolution of load with increased crack mouth opening displacement required for the estimation procedure. One key result emerging from the analyses is that levels of weld strength mismatch within the range ±20% mismatch do not affect significantly J and CTOD estimation expressions applicable to homogeneous materials, particularly for deeply cracked fracture specimens with relatively large weld grooves. The present study provides additional understanding on the effect of weld strength mismatch on J and CTOD toughness measurements while, at the same time, adding a fairly extensive body of results to determine parameters J and CTOD for different materials using bend specimens with varying geometries and mismatch levels.     

Structural integrity of pipelines: T-stress by line-spring

The elastic T‐stress is an important constraint parameter for characterizing elastic–plastic crack‐tip fields and in fracture assessment procedures. However, many of the methods reported in the literature for estimating T‐stress are not easily suited for surface‐cracked pipes because these are three‐dimensional in nature. Here, the line‐spring method is demonstrated to be an efficient and accurate tool for the constraint estimation in surface‐cracked pipes. Detailed three‐dimensional analyses are performed to verify the line‐spring results. Using the line‐spring method, the effects of different crack geometries and diameter‐to‐thickness ratio on stress‐intensity factor (SIF) and T‐stress in circumferentially surface‐cracked pipes are examined. Further, a compendium of normalised SIF and T‐stress values for surface‐cracked pipes in remote tension and bending, calculated from a total of 1000 analyses, is tabulated. Finally, the application of an ‘elastic–plastic’ T‐stress under large‐scale plasticity is explored.     

Cleavage fracture modeling of pressure vessels under transient thermo-mechanical loading

The next generation of fracture assessment procedures for nuclear reactor pressure vessels (RPVs) will combine non-linear analyses of crack front response with stochastic treatments of crack size, shape, orientation, location, material properties and thermal-pressure transients. The projected computational demands needed to support stochastic approaches with detailed 3-D, non-linear stress analyses of vessels containing defects appear well beyond current and near-term capabilities. In the interim, 2-D models become appealing to approximate certain classes of critical flaws in RPVs, and have computational demands within reach for stochastic frameworks. The present work focuses on the capability of 2-D models to provide values for the Weibull stress fracture parameter with accuracy comparable to those from very detailed 3-D models. Weibull stress approaches provide one route to connect non-linear vessel response with fracture toughness values measured using small laboratory specimens. The embedded axial flaw located in the RPV wall near the cladding-vessel interface emerges from current linear-elastic, stochastic investigations as a critical contributor to the conditional probability of initiation. Three different types of 2-D models reflecting this configuration are subjected to a thermal-pressure transient characteristic of a critical pressurized thermal shock event. The plane-strain, 2-D models include: the modified boundary layer (MBL) model, the middle tension (M(T)) model, and the 2-D RPV model. The 2-D MBL model provides a high quality estimate for the Weibull stress but only in crack front regions with a positive T-stress. For crack front locations with low constraint (T-stress < 0), the M(T) specimen provides very accurate Weibull stress values but only for pressure load acting alone on the RPV. For RPVs under a combined thermal-pressure transient, Weibull stresses computed from the 2-D RPV model demonstrate close agreement with those computed from the corresponding crack front locations in the 3-D RPV model having large negative T-stresses. Applications of this family of 2-D models provide Weibull stress values in excellent agreement with very detailed 3-D models while retaining practical levels of computational effort.     

Effect of crack depth on the shift of the ductile-brittle transition curve of steels

Nuclear reactor pressure vessel (RPV) steels degrade due to neutron irradiation during normal operation. As a result, the ductile-brittle transition curve of the steel shifts to higher temperature which decreases operation margins in both the temperature and pressure. The loss of these margins however can be offset somewhat by appealing to arguments based on constraint of potential/postulated shallow cracks. In this paper, it is demonstrated that the fracture toughness values for shallow flaws are higher than those determined from standard deep cracked test specimens based on constraint consideration. The J-A₂ three-term solution is used to characterize the crack-tip stress field where J represents the level of loading and A₂ quantifies the level of constraint. Based on the RKR cleavage model, procedures to quantify the temperature shift between specimens with different constraint levels are developed. The experimental data by Sherry et al. [Sherry AH, Lidbury DPG, Beardsmore DW. Validation of constraint based structural integrity assessment methods. Final report, Report No. AEAT/RJCB/RD01329400/R003, AEA Technology, UK, 2001] for the A533B RPV steel are used to demonstrate the procedure and it is shown that the ductile-brittle transition curve shifts to lower temperature from high constraint to low constraint specimens.